Are there any jump scares/giant sea monsters that would affect someone with thalassophobia?
I would say yes, there are jump scares, but not intentionally. Here are some instances you might get a jump scare at:
Reaper Leviathans can tend to sneak up on you. This is partly because sometimes the game doesn't spawn them right away until you are too close to really get away (I don't think this is suppose to happen, as it is odd to unfairly spawn a dangerous creature like this in front of you - it's likely a bug). They are aggressive, and can kill you fairly fast. This can be made worse if you are in a Seamoth traveling fast and all of a sudden a Reaper spawns right in front of you. Reaper Leviathans have a very noticeable sound that you can hear quite easily however.
Sand Sharks can bury themselves in the sand and pop out and bite you. Typically, this is rare, but it is possible. You can see their fin sticking out of the sand usually. Avoid going near the fin.
Sea Dragon Leviathans are a massive creature that are thankfully very far down in the ocean (~1400m+). They make a very noticeable sound and are aggressive, however the area that you run into them is very large, making avoiding them fairly easy. It would be hard to be jump scared by them as you typically can see them before they see you.
The Warper can spawn right in front of you (and this is intended). It teleports to you/around you, and can teleport you to it (even if you are in a vehicle), and attack you.
Mesmers can sometimes appear invisible looking (although I believe this is not intended), and they take control of your movement slightly. When they do this, you will begin to swim towards them automatically (which you can resist), and your suit will begin talking to you saying to swim towards the creature. If you get too close to them while they are controlling you, you will take damage.
Crabsnakes hide inside of the giant purple jelly mushrooms in the Jellyshroom Cave. They can pop out of the top of these mushrooms and attack you. Typically, you can see them sitting inside of the holes on top of the mushrooms first. Just keep your distance to avoid them.
Crashfish reside inside of their pods in the Safe Shallows. If you get too close to their pods, they open up, and begin to fly at you. They will explode after about 5 seconds of chasing you. This isn't much of a scare unless you completely miss their noticeable pods. They also make quite a lot of noise when they begin to swim at you.
Bleeders are fairly small, and latch onto the players arm and begin to deal damage. This could provide a jump scare if you don't see these small creatures and all of a sudden they latch onto you. To get them off, hit them with your other arm, or continue swimming. Holding still is not a good idea.
The rest of the hostile fauna in the game are typically easy to notice and don't really provide any sort of jump scare. You'll likely see them before they see you, and to avoid any creature, just keep your distance.
Keep your eyes peeled, and I think you will be alright. Enjoy this fantastic game!
Yes. You do. Its a survival & exploration game, and the whole game revolves around exploring dangerous places where more or less dangerous creatures reside. You will have to evade them (there is barely any weapon in the game).
Those creatures can and will sneak up on you and attack you by surprise.
Still, if you only play in sandbox mode and enjoy the base building aspect of the game, You can pretty much always stay in the "Safe Shallows" area of the game where no predators are, and have a quite uneventful but visually pleasing game.
If you have a fear of open water, Subnautica will be a pretty terrifying experience--it kind of capitalizes on that feeling. And while there are no true jumpscares, all the anticipation it naturally builds can make any mildly surprising event feel like a jumpscare.
But hear me out a bit, because I think I came from a similar place to you, yet Subnautica became one of my favorite exploration-type games.
So I similarly have a fear of vast, open water situations--not clinically confirmed or anything, but the eel situation you mentioned in SM64 was one of the most terrifying parts of my childhood, and it was many years before I was able to confront it (and even then, only on the smaller screen of the DS version!). The eel boss in Mario Sunshine gave me a lot of similar issues, and it didn't even move. Heck, there are some places in the Wind Waker that I still haven't looked at to this day because of the Sea Hat enemies and how helpless they make me feel when they knock me out of the boat, even though I know there's nothing in the water that I'm actually vulnerable to. And don't even get me started on the entire Great Bay area in Majora's Mask, particularly Pinnacle Rock and its... eel things.
I don't know how severe you've got it, but I can at least say I have an idea of where you're coming from--large, open water sections have been something I've specifically noticed I don't mentally handle well, even when in times know for a fact that nothing unexpected will happen.
Subnautica? I find it's a great balance between "it's all in your head" and fulfilling the tense expectations. You can always hear the majorly dangerous creatures from far away, long before they aggro you. (The only obstacle to this is, like others have said, improper loading speeds in the game when you're traveling at high speeds in vehicles. The only real solution is to avoid certain "danger zones" when needing to travel quickly.) Things actually sound a lot closer than they actually are, which I don't totally like, but it's a testament to how far away you're able to detect threats. Essentially, the only thing that makes it "scary" is you--it doesn't really go for any typical horror-esque tactics like waiting for you to look at a monster before it pops out to give you a spook. It's all just part of the natural flow of the game, which I've found to be incredibly entertaining.
The closest thing to "jumpscares" that really happen is when you're aware of the threat because of its sounds, trying to avoid it, looking periodically to double-check its location, then one of the times it's suddenly a lot closer than you thought. Perhaps you even looked just as it made its "I'm attacking you" noise, filling in all the elements of a "jump scare" just by coincidence.
Not all environments have potential threats, too. Most of the threats are near the ground, where I don't get the "open water terror" feel nearly as much. In fact, I pretty much keep sight of the ground at any given time, avoiding the biggest "open" spaces, since A) they freak me out, and B) there's nothing in such spaces 90% of the time. Definitely nothing useful in such spaces. And in the places where the "vast open waters" feeling still is there even when near the ground or a wall, there aren't always any actual dangers lurking about. You kind of learn which places have which dangers, which leads to this weird feeling of "these waters make me acutely uncomfortable, but I know I'm not in danger." The result is kind of this feeling of "awe," as I'm still shaken by the open water sensation, but because I'm secure in the knowledge that I'm safe, the fear is reduced to mostly a bodily impulse. It's a pretty surreal feeling that you don't get to experience much that I think Subnautica rather uniquely delivers on.
(There is a seabase piece called a "scanner room" that allows you to pilot small camera drones in a pretty wide radius around the room. Enemies mostly ignore them, so they're very useful to set up as scouting posts for seeing where the potentially-very-frightening monsters reside -- allowing you to either come up with a game plan for sneaking around them or so you know what areas to avoid altogether)
So, yeah, I came from at least a similar emotional place with a persistent fear of large open waters (open spaces in general, really, but aquatic ones are the worst), yet I've found that plays into my enjoyment of the game. I hope, if you didn't play it before when people replied months ago, you'll still give it a try. I know it doesn't help to say "it's all in your head"... but in this case, for me, that made it better!